\documentclass[UTF8]{article}
\author {Author}
\title {Title}
\usepackage{ctex}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\maketitle
\section{First section} test1.
    \subsection{First subsection} test2.
        \subsubsection{First double subsection}
            \paragraph{Fist paragraph} test3.
                \subparagraph{First subparagraph} test4.
    \subsection{Second subsection}
        \paragraph{段落} 中文测试。
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Hello World! \\ % This is comment
Hello \LaTeX ! \\

$\lim\limits_{n \rightarrow +\infty} P\lbrace\frac{\sum\limits_{i=1}{n}Xi - n\cdot EX}{ \sqrt{n \cdot DX} }  \leqslant x\rbrace = \Phi(x)$ \\

$P\lbrace a<X<b \rbrace \approx \Phi(\frac{b - n\cdot EX}{\sqrt {n\cdot DX}}) - \Phi(\frac{a - n\cdot EX}{\sqrt{n\cdot DX} })$ \\

$F(x,y) = F_{X}(x)F_{Y}(y)$
\end{document}
